An Efficient Basis-Free Loop-Star Preconditioner Using Sparse Direct Solvers

When projectors are used to formulate the loop-star preconditioning, a sparse but singular graph-Laplacian matrix must be inverted. In this article, the charge neutrality condition is enforced to remove the zero singular value of this matrix and a sparse direct solver is used to invert the result. While the formulation is low-frequency stabilized and requires few extra operations per iteration, the number of iterations remains high. The iteration count is improved by combining it with an elementdiagonal sparse preconditioner.